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Math Help - trig functions

  1. #1
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    Wink trig functions

    prove that d/dx (sec x) = sec x tan x

    im confused...
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  2. #2
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    Hello, xSMUxCHEERLEADINGx!

    Prove that: . \frac{d}{dx}(\sec x) \:=\: \sec x\cdot\tan x
    Here's one way . . .


    We have: . y \;=\;\sec x \;=\;\frac{1}{\cos x} \;=\;(\cos x)^{-1}

    Then: . \frac{dy}{dx} \;=\;\text{-}1(\cos x)^{-2}(\text{-}\sin x) \;=\;\frac{\sin x}{\cos^2\!x} \;=\;\frac{1}{\cos x}\cdot\frac{\sin x}{\cos x} \;=\;\sec x\cdot\tan x

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